On splitting and merging categories: a regression account of subadditivity

Frequency judgments tend to be subadditive: A category's frequency is judged to be lower than the summed frequency of its subcategories. Thus, by splitting or merging categories, subjective frequencies increase or decrease, respectively. We offer an account of this phenomenon that is based on the statistical principle of regression. Because empirical information is never noise-free, high frequencies are underestimated, and low frequencies are overestimated. The underlying regression principle explains available evidence on subadditivity and allows novel predictions. The findings from two experiments supported predictions derived from the regression account of frequency estimates for split and merged categories: Subadditivity varied systematically as a function of the two parameters determining regression (extremity and reliability). More extreme frequencies and reduced reliability led to increased regression effects. Theoretical implications for subadditive judgments (of frequency, probability, and/or value) are discussed. Although other factors may contribute to subadditivity, their influence needs to exceed the baseline expected from the regression model alone.